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I did this job on a small bathroom with a Fein multitool (original and still the best!). Went through a few tungsten carbide coated grout grinding specific bits. It's slow going and painful but safer than a diamond grinding disk. With the amount you have to do I would consider a diamond grinding disk on an angle grinder and very steady hand though. Way more risky but much quicker.
This is the kind of disk I used :-
I need to remove and re grout the terrace. I have a grinder but am considering getting a osculating multi tool and tool for it. Has anyone done this job? Grout is concrete about 1cm wide.